It sounds like you may have injured your hand when you punched your friend. There are several concerns with this kind of closed fist injury. I recommend that you visit your primary care physician
as it is always best to have traumas, even accidental ones, evaluated right away to protect your health for the future.
If you did break the skin, it is possible that you could develop a dangerous infection because there are many organisms in the human mouth capable of causing serious infection. In addition, there are several characteristic fractures in the bones of the hand and wrist that may not be apparent immediately after injury but that can cause persistent pain and limitations with activity, as you are describing.
The so-called boxer's fracture affects bones in the fingers, while a fracture of the scaphoid bone in the hand can also be quite debilitating (and can cause permanent damage if not allowed to heal with prolonged immobilization).
In order to make sure you don't have an occult fracture or other injury of your hand, it is important for you to see your primary care physician right away. He or she will undoubtedly arrange for x-ray
imaging of your hand, in addition to performing a physical exam. Depending upon the findings, you may need to see an orthopedic surgeon
for more definitive management.